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Can you help interpret what this interval tells us and how I can understand it?

Can you help  interpret what this interval tells us and how  I can understand it?



The 95% confidence interval for the population mean IQ is, (107.77, 116.23).

Interpretation:

We are 95% confident that the population mean IQ will be in between (107.77, 116.23).

Explanation:

The size of the sample, n = 33

The sample mean, xˉ = 112

 

The population standard deviation, σ = 12.4

Since the population standard deviation is known, use of z confidence interval

is appropriate in this scenario.

The z-critical value at 95% confidence level, z = 1.96

The margin of error is, E=z×nσ=1.96×3312.4=4.23

The 95% confidence interval for the population mean IQ is,

[xˉE,xˉ+E]=[1124.23,112+4.23]=[107.77,116.23]

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